Help Mathematical Statistics questions in matematica !!!</SPAN></SPAN>
Win a teddy bear at a dice game throws you five dice in the form of the Platonic bodies. The dice are numbered with the integers 1,2, ..., n where n is the number of pages. After throwing it summarizes the numbers on the pages are upturned, but the tetrahedron is the century (1-4) written in the tip pointing upwards.
1. Your first task is to accurately determine the probability function for the sum S and state E (S) and D (S).
At a carnival is a position where you can win a big teddy bear if you participate in the mentioned dice game. You invest €3, and then throw the five dice. If the total meets the conditions (S £ 10+S ³ 45) you win the teddy bear. The carnival valued the teddy bear at € 100 (but purchased for € 60).
2. Determine the exact probability of teddy profit and determine also the average profit that the Carnival makes per one player.
To obtain the sum of the probability of throwing five Platonic dice. I use Tuples to generate a list of possible n - Tuple of elements from the list. All possible 5 - Tuples of (1 , 4), (1, 6), (1, 8), (1, 12), (1, 20)</SPAN></SPAN>
W=Tuples[{ Range[1,4],Range[1, 6],Range[1,8],Range[1,12],Range[1,20]}]

I did the first question but not the second somewere I lost to determine the average profit that the Carnival makes per one player.